What was Jesus' purpose? Throughout the Bible God repeats phrases such as, "So you will know that I am God," and "That you may know that I am Lord," and "Then you will know I am Lord," and so forth. I believe what He finished was what the Father sent Him to do. I offer the following...
John 6:29 NKJV
Jesus answered them, “This is the work of God, that you believe in him whom he has sent.”
John 6:35-40 NKJV
Jesus said to them, “I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst. But I said to you that you have seen me and yet do not believe. All that the Father gives me will come to me, and whoever comes to me I will never cast out. For I have come down from heaven, not to do my own will but the will of him who sent me. And this is the will of him who sent me, that I should lose nothing of all that he has given me, but raise it up on the last day. For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.”
John 6:66-69 NKJV
After this many of his disciples turned back and no longer walked with him. So Jesus said to the twelve, “Do you want to go away as well?” Simon Peter answered him, “Lord, to whom shall we go? You have the words of eternal life, and we have believed, and have come to know, that you are the Holy One of God.”
John 12:44-50 NKJV
And Jesus cried out and said, “Whoever believes in me, believes not in me but in him who sent me. And whoever sees me sees him who sent me. I have come into the world as light, so that whoever believes in me may not remain in darkness. If anyone hears my words and does not keep them, I do not judge him; for I did not come to judge the world but to save the world. The one who rejects me and does not receive my words has a judge; the word that I have spoken will judge him on the last day. For I have not spoken on my own authority, but the Father who sent me has himself given me a commandment—what to say and what to speak. And I know that his commandment is eternal life. What I say, therefore, I say as the Father has told me.”
John 13:31-35 NKJV
When he had gone out, Jesus said, “Now is the Son of Man glorified, and God is glorified in him. If God is glorified in him, God will also glorify him in himself, and glorify him at once. Little children, yet a little while I am with you. You will seek me, and just as I said to the Jews, so now I also say to you, ‘Where I am going you cannot come.’ A new commandment I give to you, that you love one another: just as I have loved you, you also are to love one another. By this all people will know that you are my disciples, if you have love for one another.”
John 17:1-4 NKJV
When Jesus had spoken these words, he lifted up his eyes to heaven, and said, “Father, the hour has come; glorify your Son that the Son may glorify you, since you have given him authority over all flesh, to give eternal life to all whom you have given him. And this is eternal life, that they know you, the only true God, and Jesus Christ whom you have sent. I glorified you on earth, having accomplished the work that you gave me to do.